Naming the Unit
It will be essential for students to learn that each number they work with refers to some quantity, often called the "unit" or the "whole". Insisting students to always specify the units for any answer will help to develop "unit consciousness". Developing "unit consciousness" is key for successful fraction learning. For example when you say three, you can mean to say that you have three dogs, or three balls, or three books, or whatever you have three of. Three is describing how many you have of some understood unit. Thus, three is acting as an adjective. Dogs, balls, and books are the objects being named and are nouns that specify the unit. Knowing the unit is essential. It makes a huge difference if you have 3 cents or 3 hundred dollar bills. It makes a huge difference if you have 3 goldfish or 3 whales. This is the idea of the adjective-noun theme created by Herb Gross. 6 He has found that that using this adjective-noun theme of Math as a Second Language can make comprehension of mathematical concepts easier for students. This concept will be especially helpful for the addition of fractions with like and unlike denominators.
This idea emphasizes the importance of having the same unit when doing arithmetic. For example, if you have 3 soccer balls plus 2 soccer balls you will have a total equaling 5 soccer balls (fig. 3). However, if you have 3 soccer balls plus 2 rocket ships, you do not have a total equaling 5 soccer balls or 5 rocket ships. You still have 3 soccer balls and 2 rocket ships (fig. 4). You could say that you have 5 things total if you don't care about the difference between a soccer ball and a rocket ship. The idea is to be clear in what information you are asking for.
The key is to be precise about the unit. Practice with this is necessary for understanding the number and object relationship.
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